## Copyright (C) 2022 Nicholas R. Jankowski ## Copyright (C) 2012 Rik Wehbring ## Copyright (C) 1997-2016 Kurt Hornik ## ## This program is free software: you can redistribute it and/or ## modify it under the terms of the GNU General Public License as ## published by the Free Software Foundation, either version 3 of the ## License, or (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} hygecdf (@var{x}, @var{t}, @var{m}, @var{n}) ## Compute the cumulative distribution function (CDF) at @var{x} of the ## hypergeometric distribution with parameters @var{t}, @var{m}, and @var{n}. ## ## This is the probability of obtaining not more than @var{x} marked items ## when randomly drawing a sample of size @var{n} without replacement from a ## population of total size @var{t} containing @var{m} marked items. ## ## The parameters @var{t}, @var{m}, and @var{n} must be positive integers ## with @var{m} and @var{n} not greater than @var{t}. ## @end deftypefn ## Author: KH ## Description: CDF of the hypergeometric distribution function cdf = hygecdf (x, t, m, n) if (nargin != 4) print_usage (); endif if (! isscalar (t) || ! isscalar (m) || ! isscalar (n)) [retval, x, t, m, n] = common_size (x, t, m, n); if (retval > 0) error ("hygecdf: X, T, M, and N must be of common size or scalars"); endif endif if (iscomplex (x) || iscomplex (t) || iscomplex (m) || iscomplex (n)) error ("hygecdf: X, T, M, and N must not be complex"); endif if (isa (x, "single") || isa (t, "single") || isa (m, "single") || isa (n, "single")) cdf = NaN (size (x), "single"); else cdf = NaN (size (x)); endif ok = ((t >= 0) & (m >= 0) & (n > 0) & (m <= t) & (n <= t) & (t == fix (t)) & (m == fix (m)) & (n == fix (n))); if (isscalar (t)) if (ok) cdf = discrete_cdf (x, 0 : n, hygepdf (0 : n, t, m, n)); endif else ok &= ! isnan (x); n = n(ok); num_n = numel (n); v = 0 : max (n(:)); ## manually perform discrete_cdf to enable vectorizing with array input p = cumsum (hygepdf (v, t(ok), m(ok), n, "vectorexpand"), 2); sz_p = size (p); end_locs = sub2ind (sz_p, [1 : num_n]', n(:) + 1); p ./= (p(end_locs)); v_col_idx = min (lookup (v, x(ok)(:)) + 1, n(:) + 2); cdf(ok) = [zeros(num_n, 1), p](sub2ind (sz_p + [0,1], ... [1 : num_n]', v_col_idx)); endif endfunction %!shared x,y %! x = [-1 0 1 2 3]; %! y = [0 1/6 5/6 1 1]; %!assert (hygecdf (x, 4*ones (1,5), 2, 2), y, eps) %!assert (hygecdf (x, 4, 2*ones (1,5), 2), y, eps) %!assert (hygecdf (x, 4, 2, 2*ones (1,5)), y, eps) %!assert (hygecdf (x, 4*[1 -1 NaN 1.1 1], 2, 2), [y(1) NaN NaN NaN y(5)], eps) %!assert (hygecdf (x, 4, 2*[1 -1 NaN 1.1 1], 2), [y(1) NaN NaN NaN y(5)], eps) %!assert (hygecdf (x, 4, 5, 2), [NaN NaN NaN NaN NaN]) %!assert (hygecdf (x, 4, 2, 2*[1 -1 NaN 1.1 1]), [y(1) NaN NaN NaN y(5)], eps) %!assert (hygecdf (x, 4, 2, 5), [NaN NaN NaN NaN NaN]) %!assert (hygecdf ([x(1:2) NaN x(4:5)], 4, 2, 2), [y(1:2) NaN y(4:5)], eps) ## Test class of input preserved %!assert (hygecdf ([x, NaN], 4, 2, 2), [y, NaN], eps) %!assert (hygecdf (single ([x, NaN]), 4, 2, 2), single ([y, NaN]), eps ("single")) %!assert (hygecdf ([x, NaN], single (4), 2, 2), single ([y, NaN]), eps ("single")) %!assert (hygecdf ([x, NaN], 4, single (2), 2), single ([y, NaN]), eps ("single")) %!assert (hygecdf ([x, NaN], 4, 2, single (2)), single ([y, NaN]), eps ("single")) ## Test input validation %!error hygecdf () %!error hygecdf (1) %!error hygecdf (1,2) %!error hygecdf (1,2,3) %!error hygecdf (1,2,3,4,5) %!error hygecdf (ones (2), ones (3), 1, 1) %!error hygecdf (1, ones (2), ones (3), 1) %!error hygecdf (1, 1, ones (2), ones (3)) %!error hygecdf (i, 2, 2, 2) %!error hygecdf (2, i, 2, 2) %!error hygecdf (2, 2, i, 2) %!error hygecdf (2, 2, 2, i)